Disturbance rejection-based cluster synchronization of nonlinear complex dynamical networks with hybrid-driven mechanism

The issue of cluster synchronization and disturbance rejection of multi-weighted complex dynamical networks subject to nonlinearities and external disturbances are studied in this article. In particular, a hybrid-triggering control scheme is implemented to mitigate the burden of the network transmission according to the prespecified triggering condition, under which each node will transmit its signal independently to the controller. To be more specific, a Bernoulli distributed stochastic variable is introduced to describe the switching law of the communication scheme. Also, the disturbance rejection performance is carried out with the aid of an improved equivalent input disturbance estimator approach. The sufficient criterion in the form of linear matrix inequalities is derived by constructing a suitable Lyapunov-Krasovskii functional and employing stochastic theory. Based on these settings, the feedback gain matrices and the trigger parameters affirming the desired cluster synchronization performance of the considered networks are established. Eventually, two illustrative examples including Lur'e networks with simulations are presented, which evidently proves the effectiveness of the obtained results.